::# Axiom of choice in functional form via Fr\{ae}nkel operator
::# It is used to arbitrarily partition the field of a function f
::# into three parts, one of which is made of the fixpoints.
::# We will use this construction in Lm100 for the case of f
::# being a permutation, hence some elementary properties are shown
::# for that case.

::# Building the needed SetValuation (tohilbval), and the
::# needed permutation of it, called tohilbperm.
::# They are specifically built so to enjoy the right fixpoints properties
::# in order to prove the main theorem (Lm100).